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# Ball mill working principle and analysis of grinding body mo

## 1.The working principle of the ball mill

The main working part of the

**ball mill**is a rotary cylinder mounted on two large bearings and placed horizontally. The cylinder is divided into several chambers by the partition plate, and the grinding body of a certain shape and size is installed in each bin. The abrasive bodies are generally steel balls, steel forgings, steel bars, pebbles, gravel, and porcelain balls. In order to prevent the cylinder from being worn, a liner is placed on the inner wall of the cylinder.

Since the feed end continuously feeds the new material, the material difference between the feed and the discharge end material can force the material to flow, and the axial thrust of the impact material when the abrasive body falls also forces the material to flow, and the internal gas flow. Movement also helps the material flow. Therefore, although the mill barrel is horizontally placed, the material can be slowly flowed from the feed end to the discharge end to complete the grinding operation.

## 2.the basic state of the movement of the grinding body

The rotation speed and filling rate of the

**ball mill**cylinder have a great influence on the action of the grinding material. When the cylinder rotates at different speeds, the grinding body in the cylinder may appear in three basic states, as shown in Figure 2.2.

Figure 2.2 (a) The rotation speed is too slow. When the grinding body and material are brought to the height equal to the dynamic friction angle by the frictional force, the grinding body and the material will fall, which is called “dumping state”, which has abrasive effect on the material, but The impact of the material is very small, so the grinding efficiency is not good; Figure 2.2 (c), the speed is too fast, the grinding body and material under the action of its inertial centrifugal force

(a) low speed; (b) suitable speed; (c) high speed

The attached cylinder rotates together (for circular motion), which is called “turning state”. The grinding body does not impact and grind the material; Figure 2.2(b), the rotation speed is suitable, and the grinding body is lifted to a certain height and then thrown down. Come, called "dumping state", the grinding body has a large impact on the material and the grinding effect, and the grinding efficiency is high.

In fact, the state of motion is very complicated, the movement attached to the wall of the mill barrel; the downward sliding along the wall of the barrel and the layer of the grinding body; the falling motion of the projectile; the rotation of the axis around itself and the rolling, etc. . The basic effect of the so-called abrasive body on the material is the result of the combined action of the above various sports on the material, the main one of which can be attributed to impact and grinding.

The basic function of the grinding material is analyzed. The purpose is to determine the reasonable motion state. This is the basis for the correct selection and calculation of the suitable working speed, power, production capacity and mechanical calculation of the mill.

## 3. the ball mill internal motion analysis

The grinding effect of the

**ball mill**is mainly the impact and grinding of the grinding body on the material. In order to further understand the essence of the action of the grinding body on the material during the operation of the mill, in order to determine the working parameters of the mill, such as the appropriate working speed, power consumption, production capacity, grinding body loading and mastering the grinding mill grinding efficiency Factors, cylinder force and strength calculations, etc., must be analyzed and studied in the grinding state of the grinding body.

The actual state of the motion of the grinding body is very complicated. In order to simplify the problem analysis, the following basic assumptions are made:

(1) When the mill is in normal working, there are only two kinds of movement trajectories of the grinding body in the cylinder according to the position: one is layer by layer with the geometric center of the cross section of the cylinder as the center, according to the concentric circular path The cylinder rotates upwards; the other is to descend on a parabolic trajectory layer by layer;

(2) The relative sliding between the grinding body and the cylinder wall and between the polishing body layer and the layer is extremely small, and the specific calculation is omitted;

(3) The influence of the material in the mill barrel on the movement of the grinding body is negligible;

(4) The grinding body acts as a mass point, so the outermost radius of gyration can be expressed by the effective inner diameter of the cylinder.

The grinding body moves upward according to the circular arc with the rotation of the cylinder. When reaching a certain height, it begins to leave the circular path and falls along the parabolic trajectory. The instantaneous center of the grinding body is called the detachment point, and the layers of the grinding body are separated from the point. The line is called the breakaway point trajectory, as shown by the AB line in Figure 7.3. When the grinding body descends by a parabolic trajectory and reaches the end of the landing, the instantaneous center point of the grinding body is called the landing point, and the line connecting the falling points of each layer is called the landing point trajectory, as shown by the CD line in Figure 7.3.

## 4. The ball mill production capacity

There are many factors affecting the production capacity of the

**ball mill**, such as the nature of the material, the particle size of the milled material, the required product fineness, the uniformity of the feed and the degree of filling in the mill. It is also related to the structural form of the mill, such as the length and diameter of the mill barrel, the number of bins, the ratio of the length of each bin, the form of the partition plate and the effective section size, the type of the grinding body and the shape of the liner. The adoption of new processes and new technologies is also an effective measure to increase the mill's production capacity.

### (1) Material aspects

The material to be ground is fragile, easy to grind, and the production capacity is high; otherwise, the production capacity is low.When the particle size of the grinding material is large, the first bin of the mill must be filled with more large steel balls, so that the grinding body can achieve the purpose of crushing the material, and the first bin plays the role of the crusher to a certain extent, resulting in The grinding process is unreasonable because the crushing efficiency of the mill is much lower than that of the crusher. Therefore, reducing the particle size of the grinding can increase the productivity of the mill and reduce the power consumption.

The feeding capacity is uniform, and the feeding amount is appropriate, the grinding machine production capacity is improved. If the amount of feed is too small or too much, the production capacity should be reduced. Because the amount of feed is too small, when the abrasive body falls, not all of it impacts on the material, but some of the abrasive bodies collide with each other and make useless work; on the contrary, if the feed amount is too much, the impact energy cannot be fully exerted, and the mill production capacity is also Can't improve.

### (2) Ball mill structure

The length to diameter ratio of the mill is related to the production mode. For the mill of the open flow production system, to ensure the fineness of the product once, the length to diameter ratio is L/D=3.5~6; for the mill of the circulating flow production system, To increase the flux of materials, L/D=2.5~3.5 should be selected.

The number of warehouses in the mill is generally 2 to 4 warehouses, the larger the aspect ratio, the more warehouses. According to the production practice experience, the general dry loop production mill: when the double warehouse grinding, the first warehouse length is 30%~40% of the full length, and the second warehouse length is 60%~70 of the full length. %; Sancang mill, the first warehouse length is 25%~30% of the full length, the second warehouse length is 25%~30% of the full length, and the third warehouse length is 45%~50 of the full length. %. For mills that are produced in an open flow, the fine grinding bin should be appropriately increased in length. This is also the case when producing high-strength grades of cement, in order to increase the fine grinding time of the material and to achieve the fineness requirements of the product.

In the form of the partition plate in the mill, the number and size of the pupils of the partition plate should be appropriate. If the number of the holes is small, the size is too small, and the effective ventilation area of the partition plate is small, which increases the draft resistance and the material. The flow rate is also affected. If the number of pupils is too large or too large, the strength of the compartment board is not enough, and it is easy for the coarser particles to enter the next bin, the load is aggravated, and the work of each bin is out of balance.

The surface shape of the mill liner has a great influence on the mill output, because it can change the lifting height, that is, affect the impact of the grinding body on the material and the grinding efficiency. Therefore, the form of the lining should be chosen correctly.

The grinding efficiency of the material in the mill is also related to the type, specification, grading and filling rate. Therefore, it must be chosen correctly and reasonably.

### (3) Adopting new technologies

1 grinding system automatic control. According to the noise of the mill, the electric vibrating feeder or the belt feeder is controlled by the electric ear method, and the proper amount of the material in the mill is controlled and the material is automatically adjusted to be evenly added, so that the amount of the material in the grinding is always maintained at an optimum state, which can increase the output of the mill. .

2 Strengthen the ventilation inside the mill. The mill has a certain wind speed, so that the fine powder generated during the grinding process can be taken away by the airflow in time, which reduces the buffering effect of the fine powder, can improve the grinding efficiency, and the product quality is not affected. When the ventilation is good, the steam in the mill is discharged in time, the pores of the partition plate are not blocked, the adhesion phenomenon is also reduced, and the temperature inside the mill can be lowered, which is beneficial to the operation of the mill and the improvement of product quality. The ventilation speed in the mill varies with different materials, generally 0.3~1.0m/s. The production of high-strength grade cement should use low speed; vice versa.

3 spray water inside the mill. A lot of heat is generated when grinding cement, which is unfavorable for cement quality and grinding efficiency, and affects production. The water is atomized and sprayed into the mill with high-pressure air, effectively taking away the heat in the mill and achieving internal cooling in the mill. Water is a surface active material, which easily disintegrates the agglomerates of the particles and prevents the inclusion of the abrasive. The water spray in the mill is determined according to the temperature inside the mill, and generally does not spray water below 100 °C. In addition, the amount of water spray depends on the temperature of the clinker, which accounts for about 1% to 2% of the amount of cement, and completely evaporates the water injected into the mill without leaving moisture. It can be sprayed from the grinding head or sprayed with water. When the temperature of the milled material is very high, it is advantageous to spray water from the grinding head, and in general, it is sprayed from the tail. Spraying water inside the mill can increase the production capacity by 5%~10%.

Adding grinding aid to the mill can increase the production capacity by about 10%. Generally, triethanolamine is used, and the blending amount accounts for 0.04%~0.1% of the milled material.

### (4) Calculation of ball mill production capacity

All of the above factors affect the production capacity of the mill. So far, there is no calculation formula that can include all these factors. The exact data must be determined through production practice. Now the commonly used calculation formula is introduced as follows

Q=0.2VDnGV0.8K (7.70)

Where: Q - the capacity of the ball mill, t / h;

V——the effective volume of the

**ball mill**cylinder, m3;

D——the effective inner diameter of the cylinder, m;

K——The output per unit time of the ball mill unit power, t/(kW·h).

The output of the ball mill unit power per unit time is shown in Table 1.

Fifth, the type and material of the grinding body

## 1, type

Abrasive bodies of different shapes and sizes have different grinding effects during the grinding process. The grinding bodies used in ball mills in cement plants are mainly classified into the following types according to their shapes:

1 Steel ball Steel ball is a kind of grinding body widely used in ball mills. According to the requirements of the grinding process, steel balls of various specifications of Φ20～Φ130mm are generally selected; for the coarse grinding of the

**ball mill**, various steel balls of Φ50～Φ100mm are generally selected, and for the fine grinding bin, various steel balls of Φ20～Φ50mm are selected.

2 Steel Forging Steel forging has a short cylindrical shape, and its specifications are expressed in millimeters of diameter by length. Steel forging is generally used for fine grinding of open ball mills and for fine grinding of closed ball mills.

Commonly used steel forging specifications are Φ10mm × 10mm ~ Φ50mm × 60mm. The steel forging diameter of the small grinding mill is as small as Φ12mm×12mm.

3 Steel Bars Steel bars are an abrasive body used in rod mills. The bar specifications are expressed in millimeters of diameter by length. The diameter of the steel rod is generally Φ40～Φ90mm, and the length of the rod should be shorter than the length of the mill bar Φ50～Φ100mm. For example: Φ2.4m×13m wet baseball mill, the effective length of the first bin is 2.75m, and the specifications of the steel bar are Φ60mm×2650mm, Φ65mm×2650mm and Φ70mm×2650mm.

## 2, grinding material selection

The abrasive body should have high wear resistance and impact resistance. It is required to be hard, wear-resistant and not easily broken. The surface of the abrasive body is not allowed to have obvious burrs and cracks, and the roundness of the steel ball shall not exceed 2% of its diameter.

In the cement industry, the consumption of the grinding machine and the lining of the mill is quite large, and the quality of the grinding body not only affects the grinding efficiency of the mill, but also the operating rate of the mill. Countries around the world have made great achievements in improving wear resistance. High-chromium cast iron (steel) balls have been widely used since the 1960s and 1970s. Japan's main high-chromium steel balls, low-chromium steel balls and alloy white cast iron balls; Germany's main high-chromium cast iron balls and low-alloy steel balls; alloy steel balls commonly used in the United States and Canada.

In recent years, in China's cement industry, the grinding body materials used in

**ball mills**are as follows:

1 High-chromium cast ball High-chromium cast ball is an alloy white cast iron ball with high chromium content (Cr10% or more). Its characteristics are wear resistance, heat resistance, corrosion resistance and considerable toughness. The surface hardness HRC of the high chromium cast iron ball of the martensite matrix can reach 58-66. The wear resistance of the high chromium cast iron ball is 8 to 12 times that of the ordinary carbon steel ball.

2 Low Chromium Cast Ball The low chromium cast ball contains a small amount of chromium to maintain the pearlite metallographic white mouth. Low chrome cast ball has higher toughness and wear resistance.

3 Forged bearing steel ball Forged bearing steel ball can manufacture steel balls of various diameters, the carbon content is about 1.0%, the chromium content is about 0.5%, and the other elements are conventional. The ball consumption is higher than that of high chromium cast iron balls, but due to the low content of alloying elements, there is still a wider market for use.

The material of the steel bar of the baseball mill requires high hardness, wear resistance, continuous crushing, and no bending. It is usually rolled from 40Mn steel or 70# high carbon steel.

## 3, the reasonable load of the grinding body

(1) Formula for calculating the filling rate

The percentage of the volume of the grinding body filled in the mill to the effective volume of the mill is called the filling rate of the grinding body.

φ=VsVm×100%

Where: φ——filling rate of grinding inner grinding body, %;

Vs——the volume filled in the grinding body, m3;

Vm - the effective volume of the mill (cage), m3.

When the mill is loaded into the grinding body to verify whether its filling rate is consistent with the value specified in the ball-matching scheme, or when the grinding machine is worn, some steel balls and steel forging are added after the grinding body is worn, and the actual measurement and table look are commonly used. Method to calculate the amount of filling. The method is to measure the effective inner diameter Di of the mill with a ruler in the absence of material or only a small amount of material in the mill; then measure the vertical distance H from the polished body surface to the top liner through the center of the mill, and then calculate H/Di Value, the relationship is as follows (Figure 11).

Φ=β360-sinβ2π

h=Di2cosβ2

H1=Di2-h=Di21-cosβ2

Where: φ——milling body filling rate;

Β—the center angle of the grinding body filling surface to the center of the mill;

H——the distance from the center of the mill to the filling surface of the grinding body, m;

Di——the effective inner diameter of the mill, m;

H1——the height of the filling surface of the grinding inner grinding body, m.

The calculated H/Di values are listed in Table 7.2.

For mills with a grinding body filling rate greater than 32%, the following empirical formula can also be used to directly calculate the filling rate.

Φ0=113-126Hdi

Where: φ0——filling rate of grinding inner grinding body, %.

When measuring the height of the surface of the grinding body in the grinding machine, attention should be paid to the filling of the material in the grinding. If the material surface is 15 to 20 mm above the grinding body, the calculated filling rate should be subtracted by 2% to 4%.

Grinding rate has a great influence on the grinding efficiency of the mill. If the filling rate of the grinding body is too high or too low, the grinding efficiency of the mill will be reduced.

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